Numerical Approach to Central Limit Theorem for Bifurcation Ratio of Random Binary Tree

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Central and Local Limit Theories in Markov Dependent Random Variables

Limit distribution of the degrees in scaled attachment random recursive trees

We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor iX_i floor$ where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random variables, with support in [0,...

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

A Comparative Study on the Formability Prediction of Two-Layer Metallic Sheets

Two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on Marciniak-Kuczynski method associated Hill’s non-quadratic yield criterion. Formin...